I know BMW doesn't recommend rotating tires but what about switching the tires on the same axle from one side to the other? Our cars don't come with directional tires. Not that my tires look uneven but I imagine it would balance the wear more evenly.

Unless yours has some non OEM tires, the tires are asymmetrical and cannot be rotated that way. On the sidewall of the tire it clearly states "outside."

By just switching the tires from side to side, the same "outside" of say the left front tire will still remain on the outside on the right front. I'm not talking about R&R the tires from the rims. The only difference is the tire will now rotate in the opposite direction.